Generally, it is old to provide a well safety valve, such as shown in U.S. Pat. No. 3,782,461 which generally controls the fluid flow in a well conduit by means of a valve which is movable between an open and closed position in which means are provided to move the valve towards a normally closed position, and a control pressure is exerted from the well surface to move the valve towards an open position. However, in some instances it is desirable to close the safety valve when the fluid control pressure exceeds a preset value. This feature of closing on abnormally high control pressure is particularly advantageous if the annulus formed by the well tubing outside diameter and the casing internal diameter serves as the conductor for the control fluid. For example, a tubing leak into this annular space could cause a high pressure to be exerted onto the safety valve to maintain it in the open position and prevent it from closing.